Lots of good information already, so I'm not sure what I can add, but you asked for personal experience and how we started, so I'll give you my two cents...
I started with a 32 unit apartment complex with 7 other investors and myself as the deal sponsor. I am self-managing (no management company), but have leasing and maintenance staff on site. Things are going very well, but it has been a learning experience! I studied, researched, interviewed other owners, studied, studied, and studied some more for almost a year before making the offer, and still learn new things every day.
I would absolutely NOT start the same way without someone who was VERY experienced guiding me. There are just far too many ways to get in trouble. I know people who have done it, but I would never have attempted it. Analyzing the deals without a lot of study/experience is too dangerous. I can't tell you how many properties I looked at that I thought were great deals, only to run it by experienced people who showed me why it was exactly the opposite. Beyond that, knowing what kind of rehab is worth the money, knowing the market, leasing knowledge (laws/sales/customer service, etc), and any number of other things could immediately sink you.
Now what others have said is also very true -- bigger is easier. If I had found an 80-100 unit, the property could better support a professional management company that takes all of the above items out of my hands. I chose to start with the 32 and self manage so that when I do buy the next one, I'll be much better equipped to manage the management company.
The last thing I'll mention, and its already been said, is that getting an offer accepted on an 80-100 unit property as a first timer is going to be difficult unless you have extremely strong financials.
I know all those things sound contradictory, but thats been my experience. Hopefully at least something was helpful!